It’s a raw, foggy day in January, but the atmosphere at Durgin-Park is warm and inviting. Customers eager for a taste of Boston dining history squeeze inside the lobby entrance, waiting at the foot of the stairs to be seated. Tucked snugly into the concave North Market building at Faneuil Hall, Durgin-Park is well-regarded for its offerings of fresh New England fare, like pot roast, baked scrod and clam chowder.

Since news broke that Durgin-Park would close on Jan. 11, the restaurant -- one of Boston’s oldest, first opened in 1827 -- has seen a boom in business. The kitchen ran out of food on Friday, Saturday and Sunday as customers waited for hours in lines stretching down the red brick pathway on North Market Street.

“They’ve come out of the woodwork, hundreds and hundreds and hundreds of people,” Head waitress Gina Schertzer says at a back corner table at Durgin-Park, where she has worked for 43 years. “This is the grand dame of Boston. It is, in my opinion. I love it and I’ll fight ’til the end, and I don’t care who’s upset with me. It doesn’t matter. I’m a 76-year-old Sicilian woman.”

She remembers Durgin-Park in its heyday, when she was the restaurant’s first female bartender. There were three restaurant hosts, and three lines to get in: two at the back, along the brick facade on Clinton Street, and one out front on North Market Street. For a long time there were few other restaurants around. In the 1990s, when new eateries sprung up around Faneuil Hall and the competition crept in, Durgin-Park’s popularity slowly began to sink.

The age and history of the beloved dining spot, named for its founders John Durgin and Eldridge Park, are part of its charm -- and part of its problem. The upkeep of an aging building, combined with rising costs in minimum wage, liability insurance, medical insurance and food supply, meant the restaurant was fighting a losing battle, according to its owner, Ark Restaurants Chief Executive Officer Michael Weinstein.

“We see it as, for us, a no-win situation,” Weinstein said. “No one wants to see this thing close...but I’m not put on earth to subsidize a restaurant that’s not working, and don’t believe could work, under our own ownership.”

In Massachusetts, New York and Washington D.C., Weinstein described the financial environment for operating a restaurant as “hostile.” Despite a push to spend what the CEO described as “a ton of money” on advertisements and social media in the last year, Durgin-Park was failing. As leader of a publicly traded restaurant chain, Weinstein said his company had shareholders to answer to.

This week, restaurant staff began preparations to auction off the bits of memorable history framed along the walls: old news and magazine clippings, paintings, superlative awards. Before the artifacts could be stripped from the walls, Patricia Reyes, the manager of Durgin-Park, notified her staff to keep everything just where it was. She said a few potential restaurant buyers had emerged, according to Schertzer.

But those few potential buyers -- some from Massachusetts and one restaurateur in New York -- have expressed only slight interest, Weinstein said.

“We’ve had several calls, we don’t know how serious they are yet,” Weinstein said. “I don’t look at that as real until someone shows up and says ‘I have a real interest.’”

Perhaps the biggest obstacle facing the historic restaurant is its loss of customers, something Weinstein blames in part on declining foot traffic around Faneuil Hall, new competition over in the Seaport District and a new generation of consumers who simply did not grow up with Durgin-Park.

Weinstein said Ark Restaurants will remain as tenant of the property for the next month or so, and that the company is willing to meet with any interested buyers.

“If they want to meet, we’re available,” Weinstein said. “We’re not going to hand the keys over, we’re still paying rent and we’ll see how it plays out.”

As for Schertzer, the mission to keep Durgin-Park alive is more personal.

The veteran waitress first came to Durgin Park when it was purchased by her friends, the Kelley family, in the 1970s. Martin Kelley, of Quincy, Eugene Kelley, of Milton, Kevin Kelley, of Norwell, and Michael Solimando Jr. -- a real estate developer later drawn into Winter Hill gangster activities -- bought the restaurant from its former ailing owner, James Howard. They co-owned Durgin-Park for three decades before selling to Ark Restaurants.

Last week, following the news Durgin-Park was set to close, Martin Kelley’s daughter gave Schertzer a portion of her father’s ashes (Kelley died in 2008). The waitress now carries the ashes in a zip-close bag in her chest pocket -- a symbolic gesture through which she hopes Kelley, a “dear friend for over 50 years,” will bring good luck to Durgin-Park.

“I hope it all goes through and I hope that this restaurant is alive long after I’m gone,” Schertzer said. The restaurant is iconic in Boston, like Fenway Park or the Bunker Hill Monument, she added.

But even Schertzer, with her unwavering faith in the restaurant’s potential, admits Durgin-Park needs work.

Perhaps bringing back a less expensive lunch menu, she said: “a little tweak here and a tweak there.” The restaurant, though charming in its homey appeal, appears dated. Speckled across the second-floor restaurant area are red-and-white-checkered tablecloths masking old wooden tables and mismatched chairs on the hardwood flooring. Seated customers are first provided pitchers of water, perhaps by one of the few servers who have kept alive the restaurant’s tradition of tongue-in-cheek service.

The sassy tradition goes back to Durgin-Park’s opening in the early 19th century, when overnight workers would come in to drink early in the morning.

“They would give the service a ration of garbage and after a while, the service reached a saturation point and started giving it back. It stuck. And people came in looking for the abuse. It was never meant to offend anyone. It was all done in fun,” Schertzer said, admitting in today’s world, they have to act cautiously with their jokes, “because it’s a different time.”

Only four waitresses, including Schertzer, are among those who still give customers a ribbing.

“You know, the waitresses used to be surly back in the day, but they kind of mellowed down a little bit now,” says customer John Jarvis, of Winthrop, who recently visited the restaurant for lunch with his father Fred.

Jarvis brought a screwdriver hoping to take with him one of the many decorative artifacts on the walls.

“You know, like the old Garden, people were taking chairs out of the old Garden,” he said, but admitted he came out with nothing at Durgin-Park.

“They’re bolted into the wall pretty good,” he laughed. Instead, Jarvis opted to buy two $40 Durgin-Park bean pots, one for him and one for his sister who lives on Cape Cod.

He remembered the restaurant in its glory days, in the ‘80s: “back in the day, you know, Durgin-Park, mad food, mad drinks,” Jarvis said.

His father chimed in, “It’s a part of Boston history, it’s like an antique, you know.”